Finite Gr\"obner bases for quantum symmetric groups
Quantum Algebra
2025-03-20 v1 Rings and Algebras
Abstract
Non-commutative Gr\"obner bases of two-sided ideals are not necessarily finite. Motivated by this, we provide a closed-form description of a finite and reduced Gr\"obner bases for the two-sided ideal used in the construction of Wangs quantum symmetric group. In particular, this proves that the word problem for quantum symmetric groups is decidable.
Cite
@article{arxiv.2503.15104,
title = {Finite Gr\"obner bases for quantum symmetric groups},
author = {Leonard Schmitz and Marcel Wack},
journal= {arXiv preprint arXiv:2503.15104},
year = {2025}
}